Question

Use the graph to derive the equation y=mx for a line through the origin. Simplify the numerical coefficient, if needed. (1 point) Responses y=8x y equals 8 x y=x y equals x y=3x y equals 3 x y=33x y equals Start Fraction 3 over 3 End Fraction x

Answer 1

To derive the equation \( y = mx \) for a line through the origin, we need to determine the slope \( m \) based on the graph you are referring to.

Since I don't have access to the actual graph, I can guide you on how to derive the equation based on the slope you observe:

1. Identify two points on the line that passes through the origin (0,0).
2. Use the formula for the slope \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
3. If you find that the slope \( m \) equals 8 based on your observations, then the equation is \( y = 8x \).
4. If the slope \( m \) equals 1, then the equation is \( y = x \).
5. If \( m \) equals 3, then the equation is \( y = 3x \).
6. If the slope is 33, the equation will be \( y = 33x \).
7. If the slope simplifies to \( \frac{3}{3} \), it will simplify to \( 1 \), leading to the equation \( y = x \).

Based on the options you provided, if the slope was determined to be 8, 1, 3, or a repeat of 1 from the simplification of \( \frac{3}{3} \), the responses would be:

- \( y = 8x \)
- \( y = x \)
- \( y = 3x \)

Please choose the correct option depending on the slope of the line you identified.